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On the Optimality of a Dominant Unit of Account∗ On the Optimality of a Dominant Unit of Account¤ Matthias Doepke Martin Schneider Northwestern University Stanford University June 2009 Abstract We develop a theory that gives rise to an endogenous unit of account. Agents enter into non-contingent contracts with a variety of business part- ners. Trade unfolds sequentially and is subject to random matching. By using a unified unit of account, agents can lower their exposure to relative price risk, avoid costly default, and create more total surplus. We discuss the use of a unified unit of account in intertemporal trade and the robustness of a unit of account when there is aggregate price-level uncertainty. ¤Preliminary and incomplete. Financial support from the National Science Foundation (grant SES-0519265) and the Alfred P. Sloan Foundation is gratefully acknowledged. Doepke: Depart- ment of Economics, Northwestern University, 2001 Sheridan Road, Evanston, IL 60208 (e-mail: [email protected]). Schneider: Department of Economics, Stanford University, Landau Economics Building, 579 Serra Mall, Stanford, CA 94305 (e-mail: [email protected]). 1 Introduction An important function of money is to serve as a unit of account. Within countries, contracts tend to be denominated in a common unit. Most often, the medium of exchange also serves as the unit of account. However, the function of unit of account is logically separate from money’s role as a medium of exchange. In addition, there are many examples of the use of a unit of account that is different from the medium of exchange. In some cases, the currency of another country can serve as a unit of account. One example of this is the use of the U.S. dollar in foreign trade relationships not involving the United States. There are even examples of units of accounts that do not correspond to the medium of exchange of any country. Well-known example include the livre tournois in France, which was used as a unit of account for many years even when no corresponding coin was in circulation, and the ECU (European Currency Unit), which was based on a basket of European currencies and served as a unit of account in European Trade before the introduction of the Euro. Most models of money focus on the medium-of-exchange role of money. In con- trast, this paper develops a theory of the emergence of a unified unit of account. In our view, a key function of a unified unit of account is to lower relative-price risk in agents’ balance sheets. Production often takes place in chains, where pro- ducers enter into various contracts with both their suppliers and their customers. We describe an environment where such contracts are non-contingent, and where default is costly. In addition, contracting is non-synchronized, in the sense that agents meet their business partners sequentially and do not know everybody who they will interact with when contracting starts. We show that in such an environment, the adoption of a unified unit of account can serve to minimize relative-price risk, leading to more opportunities for trade and less need for col- lateral. Our work is related to a small literature on the optimality of nominal contracts. Jovanovic and Ueda (1997) consider a static moral hazard problem in which nom- inal output is observed before the price level (and therefore real output) is re- vealed. In addition, contracts are not negotiation proof, so that principal and 1 agent have an incentive to renegotiate after nominal output is observed. In par- ticular, in the optimal renegotiation-proof solution the principal offers full insur- ance to the agent once nominal output is known. This implies that the real wage depends on nominal output, so that the contract can be interpreted as a nomi- nal contract. Freeman and Tabellini (1998) consider an overlapping-generations economy with spatially separated agents in which fiat money serves as a medium of exchange. The authors show that under several particular circumstances it is then also optimal to use fiat money as a unit of account. Unlike these papers, in our theory neither delays in observation of prices or the use of money as a medium of exchange plays any role. Instead, we emphasize the use of a uni- fied unit of account to lower the relative-price risk that economic agents carry on their balance sheets, leading to more possibilities for exchange and less need for collateral. 2 The Model 2.1 Environment The model economy extends over two dates, 0 and 1. The economy is populated by two groups of agents, farmers and artisans. There is a finite set © of different types of farmers enumerated by A; B; : : : as well as a finite number n of different types of artisans enumerated by 1; 2; : : : n. There is a continuum of agents of each type; the mass of type i agents is denoted ¹i. An individual agent is identified by a pair (i; ¶), where ¶ 2 [0; ¹i]. The size of the set © and the number of artisans will be specified below when we study specific examples. Each agent is endowed with one unit of labor at date 0. Each type has a tech- nology that uses labor to make a good that is specific to him. We label a good by the type who produces it, that is, there are farm goods A; B; : : : and artisanal goods 1; 2;:::. An artisan makes his specific artisanal good one-for-one from la- bor. A farmer can use one unit of labor to produce 1 + θ units of his specific farm good. Instead of making his specific good, an agent may also use labor one-for- one to produce a numeraire good 0. Labor allocated to making the specific good 2 is denoted h and must be either zero or one; the remaining time 1 ¡ h is enjoyed as leisure. In some examples below, we also assume that an agent of type i is endowed with ki units of good zero that can be stored at no cost until date 1. The key difference between farmers and artisans is in how their specific goods are sold. Farm goods can be sold in a spot market that opens at date 1. In the spot market, farm good i can be exchanged into good 0 at price pi. The price pi is stochastic and given exogenously. The vector of all farm good prices is denoted by p. In contrast, artisans produce customized goods for a particular customer. At date 0, before production takes place, every artisan (i; ¶) is matched to one potential customer. If the artisan agrees to make and supply his artisanal product to the matched customer at date 1, no other agent can obtain utility from that product at date 1. In particular, an artisan cannot produce artisanal products for himself. The details of the matching process are described below. For now, we summarize the outcome of matching by a function c, where c(i; ¶) denotes the index pair of agent (i; ¶)’s customer. Since matching will be one-to-one, there is an inverse function s such that s(i; ¶) identifies an agent’s potential supplier of an artisanal good. The role of artisans and artisanal goods in the model is to generate a need for credit. Indeed, an artisan must commit to work at date 0 to produce the cus- tomized (nontradable) good at date 1. Moreover, the customer does not have sufficient tradable goods at date 0 to pay for the customized good up front. Ex- change must thus be arranged through a system of forward contracts. The role of farmers and farm goods in the model is twofold. First, farm goods have quoted prices, so that contract can be denominated in farm goods. In contrast, the cus- tomized artisanal goods are not traded in spot markets and contracts cannot be denominated in them. Second, farmers are naturally exposed to aggregate risk induced by price volatility.1 Price risk will matter because default on forward contracts is costly. Our analysis will consider how exchange can be organized in the economy to optimally deal with price risk. 1Price volatility is the only source of aggregate risk in our model. In addition, there is idiosyn- cratic risk from the matching process, to be discussed below. 3 The utility function of a type i agent (farmer or artisan) is given by: Xn u(x0; x; h) = x0 + (1 + θ) xl ¡ h: l=1 Here x0 is consumption of numeraire good and xl is consumption of the cus- tomized good produced by artisan l. Since every agent will be matched to one supplier, a feasible allocation has an agent (i; ¶) consume a positive amount of at most one artisan good, namely that produced by his supplier s(i; ¶). Given that the utility cost of production is one, assuming θ > 0 ensures that producing artisan goods in a match is optimal. Since all agents in the model are risk neutral, a concern with price risk will arise exclusively from costs of default. We have also assumed that no agent consumes farm goods. One interpretation is that farm goods are monies, and that farmers actually produce other goods that they sell to agents outside the model in ex- change for money. As a result, their revenue is in money. The exogenous farm prices would then represent exchange rates between different monies and good 0. A feasible allocation must respect the technology of the agents as well as the outcomes of the matching process. The latter generates a network that links sup- pliers and customers at date 0, and prohibits trades of artisanal goods except through those links.
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